Definition : Image Stabilisation
Image stabilisation helps takes sharper pictures. Keeping the camera steady when using a slow shutter speed is a challenge. This is particularly true with longer lenses or greater magnification. The recommended shutter speed to take a relatively sharp picture is 1/(effective focal length) seconds.
When using a 50mm lens on a full frame body, this means 1/50 second. When using an APS-C camera body with the same focal length the resulting recommended shutter speed is 1/(50 * 1.5) or 1/75 second or higher. Image stabilisation helps get sharper pictures when the shutter speed is slower than this recommended speed.
Image Stabilisation type
Image stabilisation is often performed at the sensor level in compact camera. In larger DSLR, Image stabilisation is more prevalent on the lenses. Telephoto lenses are usually bigger. They need a bigger mechanism to be efficient. The last generation of lenses achieves regularly 3 stops of image stabilisation compared to 1 stop when the technology initially appeared on the market.
A 200mm lens with 3 stops image stabilisation should do like a 25mm lens. The proper calculation is =(1/200)/2/2/2 or 1/25 second recommended speed.
Image stabilisation affect only camera shake when handholding the camera. A moving object in front of a 200mm lens still needs a faster shutter speed than the same object in front of a 50mm lens.
The challenge greater magnification associated with macro-photography is like longer focal length. Handholding a camera with its lens at a 1:1 magnification is also a challenge.
You can learn more about image stabilisation mechanism over here.